benchmarkfcns.dejongn5

benchmarkfcns.dejongn5(arg0: Annotated[numpy.typing.NDArray[numpy.float64], '[m, n]', 'flags.c_contiguous']) → Annotated[numpy.typing.NDArray[numpy.float64], '[m, 1]']

Computes the value of the De Jong N. 5 benchmark function (Shekel’s Foxholes). SCORES = dejongn5(X) computes the value of the De Jong N. 5 function at point X. dejongn5 accepts a matrix of size M-by-2 and returns a vetor SCORES of size M-by-1 in which each row contains the function value for the corresponding row of X. Properties:

  • Global minimum: approx 0.998004

  • Location of global minimum: (-32, -32)

  • Number of dimensions: 2

  • Recommended domain: [-65.536, 65.536]^2

  • Modality: multimodal (25 local minima/foxholes)

Mathematical Definition

\[f(x_1, x_2) = \left[ 0.002 + \sum_{i=1}^{25} \frac{1}{i + (x_1 - a_{1i})^6 + (x_2 - a_{2i})^6} \right]^{-1}\]

Visualization

../_images/dejongn5fcn.png